Dirichlet character χ736(49,⋅)\chi_{736}(49,\cdot)

• Label: 736.49
• Modulus: $736$
• Conductor: $184$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$736$
Conductor:	$184$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{184}(141,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 736.x

$\chi_{736}(49,\cdot)$ $\chi_{736}(81,\cdot)$ $\chi_{736}(177,\cdot)$ $\chi_{736}(209,\cdot)$ $\chi_{736}(305,\cdot)$ $\chi_{736}(561,\cdot)$ $\chi_{736}(593,\cdot)$ $\chi_{736}(625,\cdot)$ $\chi_{736}(657,\cdot)$ $\chi_{736}(721,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	22.22.14741666340843480753092741810452692992.1

Values on generators

$(415,645,97)$ → $(1,-1,e\left(\frac{8}{11}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 736 }(49, a)$	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$

Gauss sum

Jacobi sum

Kloosterman sum